The spin relaxation due to the spin-orbit interaction (SOI) is studied theoretically in a quantum well with electrons occupying only the ground subband. First, it is shown that the coefficient of the Rashba SOI is proportional to b(off) - 1, in which the parameter boff, determined by the band offsets and the band gaps, passes through unity, for example, by changing x in Ga0.47In0.53As(well)/AlxGa1-xAsySb1-y (barrier). Second, it is derived that the transition matrix element of each spin-flip phonon scattering has the same proportionality factor b(off) - 1, in addition to the impurity scattering previously studied by the same authors [Phys. Rev. B 89, 075314 (2014)]. These findings suggest the possibility of strongly suppressing the spin-relaxation rate by choosing appropriate materials.